Finite Group Databasebeta

?

← Prev (#514010) Next (#514012) →

C₂×#13846 #514011

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

4338 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

(1,2);(7,8,9,10)(11,12)(13,16)(14,15)(17,18)(19,20)(21,24)(22,26)(23,25);(3,4)(5,6)(12,15)(16,18)(19,21,23,22)(20,24,25,26);(4,6)(19,22,23,21)(20,24,25,26);(11,13,14,17)(12,16,15,18)

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 421207);